Real Estate Exam Math Tips — Practice Problems & Shortcuts

Real estate exam math covers commission splits, prorations, cap rate, GRM, LTV, and area calculations — and every one of these topics appears as a calculation question on the real estate license exam. Math questions make up 10-15% of most state exams, so mastering these formulas directly impacts your passing score. This page is a collection of practice problems with worked solutions — for the core formulas and definitions behind each topic, see our real estate math formulas reference. The problems below cover commissions, prorations, property valuation, lending ratios, and area measurements, and most exams provide an on-screen calculator for these calculations.

Commission Calculation Practice Problems

Commission practice problems test your ability to apply the sale price, rate, and split formulas that appear on the real estate license exam.

Problem 1: A home sells for $350,000. The total commission rate is 6%, split equally between the listing and selling brokerages. The listing agent has a 70/30 split with their broker. How much does the listing agent earn?

Total commission: $350,000 × 0.06 = $21,000
Listing brokerage side: $21,000 ÷ 2 = $10,500
Listing agent share: $10,500 × 0.70 = $7,350

Exam tip: Always calculate total commission first, then split between brokerages, then split between broker and agent — three separate steps.

Problem 2: A seller wants to net $280,000 after paying a 5% commission. What must the sale price be?

Sale price = Net ÷ (1 − commission rate)
$280,000 ÷ (1 − 0.05) = $280,000 ÷ 0.95 = $294,737 (round up)

Exam tip: When finding sale price from net, divide by (1 minus commission rate) — never subtract the percentage from the net.

Problem 3: An agent earns $4,200 from a sale. The agent’s split is 60%, and the total commission rate was 7%. What was the sale price?

Agent share ÷ agent split = brokerage side: $4,200 ÷ 0.60 = $7,000
Assume 50/50 brokerage split: $7,000 × 2 = $14,000 total commission
Total commission ÷ rate = sale price: $14,000 ÷ 0.07 = $200,000

Exam tip: Reverse commission problems require working backward through each split level — start with the agent’s check and divide your way back to the sale price.

For a complete breakdown of commission formulas and split structures, see our guide on commission calculations.

Proration Practice Problems

Proration practice problems require calculating daily rates and counting calendar days — skills tested on every version of the real estate license exam.

Problem 1 (Tax proration — arrears): Annual property taxes are $4,380. Closing date is April 15. Using the 365-day method, how much does the seller owe the buyer?

Daily rate: $4,380 ÷ 365 = $12/day
Seller responsible: Jan 1 – Apr 14 = 104 days
Seller owes buyer: 104 × $12 = $1,248

Problem 2 (Tax proration — prepaid): The seller prepaid $3,650 in annual taxes on January 1. Closing is September 1. How much does the buyer credit the seller?

Daily rate: $3,650 ÷ 365 = $10/day
Buyer responsible: Sep 1 – Dec 31 = 122 days
Buyer credits seller: 122 × $10 = $1,220

Problem 3 (Rent proration): Monthly rent is $1,800. Closing is on the 10th of the month. The seller already collected full rent. How much does the seller credit the buyer?

Daily rate: $1,800 ÷ 30 = $60/day
Buyer owns from day 10: 21 days remaining
Seller credits buyer: 21 × $60 = $1,260

Exam tip: Always determine whether the expense is prepaid or in arrears FIRST — this tells you who credits whom.

For the complete proration formula reference and additional day-count examples, visit our prorations guide.

Property Valuation Practice Problems

Property valuation practice problems test cap rate and GRM calculations — two formulas that identify income property value on the real estate license exam.

Problem 1 (Cap rate — find value): A property generates $48,000 in annual net operating income (NOI). The market cap rate is 8%. What is the property value?

Value = NOI ÷ Cap Rate
$48,000 ÷ 0.08 = $600,000

Problem 2 (Cap rate — find rate): A property sold for $500,000 and produces $35,000 NOI. What is the cap rate?

Cap Rate = NOI ÷ Value
$35,000 ÷ $500,000 = 7%

Problem 3 (GRM): A rental property has gross monthly rent of $2,500. The GRM for the area is 120. What is the estimated value?

Value = Monthly Rent × GRM
$2,500 × 120 = $300,000

Exam tip: Cap rate uses NET operating income (after expenses). GRM uses GROSS rent (before expenses). Never mix them.

For detailed coverage of the income capitalization approach and how cap rate fits into property appraisal, see our dedicated article.

Lending Ratio Practice Problems

Lending ratio practice problems focus on LTV and DTI — two ratios that determine loan eligibility and PMI requirements on the real estate license exam.

Problem 1 (LTV): A buyer purchases a home for $400,000 and makes a $60,000 down payment. What is the LTV ratio? Will the buyer need PMI?

Loan amount: $400,000 − $60,000 = $340,000
LTV = $340,000 ÷ $400,000 = 85%
Since LTV exceeds 80%, the buyer will need PMI.

Problem 2 (DTI): A buyer earns $6,000/month gross income. Monthly housing expenses (PITI) are $1,500. Other monthly debts are $300. What are the front-end and back-end DTI ratios?

Front-end DTI = $1,500 ÷ $6,000 = 25%
Back-end DTI = ($1,500 + $300) ÷ $6,000 = 30%
Conventional guideline: 28% front-end, 36% back-end — this buyer qualifies.

Exam tip: LTV determines PMI requirement (over 80% = PMI needed). DTI determines loan qualification — front-end is housing only, back-end includes all debts.

For a full explanation of LTV, DTI, and PMI and how lenders use these ratios to approve mortgage applications, see our lending guide.

Area and Measurement Practice Problems

Area and measurement practice problems test square footage and acreage conversions — straightforward multiplication that earns free points on the real estate license exam.

Problem 1 (Square footage): A rectangular lot measures 150 feet by 200 feet. What is the area in square feet and in acres?

Area = 150 × 200 = 30,000 sq ft
Acres = 30,000 ÷ 43,560 = 0.689 acres

Problem 2 (Irregular shape): An L-shaped building has two sections: Section A is 40 ft × 30 ft and Section B is 20 ft × 25 ft. What is the total square footage?

Section A = 40 × 30 = 1,200 sq ft
Section B = 20 × 25 = 500 sq ft
Total = 1,700 sq ft

Exam tip: Break irregular shapes into rectangles, calculate each, then add. Remember: 1 acre = 43,560 sq ft.

For legal descriptions and how measurements connect to property boundaries, see our article on metes and bounds.

Math Shortcuts That Save Time on the Exam

Math shortcuts help candidates solve real estate exam questions faster and reduce calculator errors under time pressure.

The T-bar method — Draw a T shape: put the part (commission, interest, tax amount) on top, rate on the bottom-left, and the whole (sale price, loan amount, assessed value) on the bottom-right. Cover what you need to find. If you need the top, multiply the two bottom numbers. If you need either bottom, divide the top by the other bottom. This single tool works for commission, interest, and tax problems.
Percentage to decimal — Move the decimal point 2 places to the left. 6% = 0.06. 5.5% = 0.055. 0.75% = 0.0075. Converting before you start calculating prevents the most common exam math error.
Finding sale price from net — Divide by (1 − rate), never add the percentage to the net amount. This applies to commission net-to-seller, tax net, and any “what must the price be” question.
Quick proration estimate — Annual amount ÷ 12 = monthly rate. Then adjust for partial-month days. This mental estimate helps you spot incorrect calculator entries before submitting your answer.
Acres shortcut — Divide square feet by 43,560 to convert to acres. A useful benchmark: a half-acre is approximately 21,780 sq ft, so any lot under 22,000 sq ft is less than half an acre.
Cap rate inverse relationship — If NOI stays the same and cap rate goes UP, property value goes DOWN. If cap rate goes DOWN, value goes UP. This inverse relationship is tested as a conceptual question, not just a calculation.

Can You Use a Calculator on the Real Estate Exam?

Yes — most state real estate exams provide an on-screen calculator built into the testing software, and candidates are not allowed to bring personal calculators. Both PSI and Pearson VUE testing platforms include a basic on-screen calculator that handles addition, subtraction, multiplication, and division — no scientific functions are available. Some states may allow a handheld calculator provided by the testing center, so check your state’s exam handbook for specific rules. Practice using an on-screen calculator before exam day to avoid wasting time clicking buttons instead of typing numbers — the interface is slower than a physical calculator, and timed exams penalize hesitation.

Test Your Knowledge — Free Practice Exam

Put these math skills to the test with our free real estate practice exam — featuring commission, proration, and valuation questions modeled after the actual licensing exam. Set a timer and work through the math section under realistic conditions to build the speed and accuracy you need on exam day.

This information is for educational purposes. Requirements may change — always verify with your state’s Real Estate Commission.